Sur la fonction Zêta associée au Laplacien singulier ${\Delta }_{{\mathcal{O}(m)}_{\infty }}$

Abstract

In a previous paper, we computed the spectrum of the singular Laplacian attached to canonical metrics on ${\mathbb{P}}^1$. In this article, we study ${\zeta }_{\infty }$, the Zeta function associated to this spectrum. We prove that it admits a meromorphic continuation to $\mathbb{C}$. Moreover, this continuation is holomorphic at zero. We compute ${\zeta }_{\infty }(0)$ and ${\zeta }_{\infty }^{\prime }(0)$.

55 pages

Cited by in corpus (1)

• Spectre du Laplacien singulier associé aux métriques canoniques sur ${\mathbb{P}}^1$